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185 lines
28 KiB
JSON
185 lines
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"title": "Count Fertile Pyramids in a Land",
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"content": "<p>A farmer has a <strong>rectangular grid</strong> of land with <code>m</code> rows and <code>n</code> columns that can be divided into unit cells. Each cell is either <strong>fertile</strong> (represented by a <code>1</code>) or <strong>barren</strong> (represented by a <code>0</code>). All cells outside the grid are considered barren.</p>\n\n<p>A <strong>pyramidal plot</strong> of land can be defined as a set of cells with the following criteria:</p>\n\n<ol>\n\t<li>The number of cells in the set has to be <strong>greater than </strong><code>1</code> and all cells must be <strong>fertile</strong>.</li>\n\t<li>The <strong>apex</strong> of a pyramid is the <strong>topmost</strong> cell of the pyramid. The <strong>height</strong> of a pyramid is the number of rows it covers. Let <code>(r, c)</code> be the apex of the pyramid, and its height be <code>h</code>. Then, the plot comprises of cells <code>(i, j)</code> where <code>r <= i <= r + h - 1</code> <strong>and</strong> <code>c - (i - r) <= j <= c + (i - r)</code>.</li>\n</ol>\n\n<p>An <strong>inverse pyramidal plot</strong> of land can be defined as a set of cells with similar criteria:</p>\n\n<ol>\n\t<li>The number of cells in the set has to be <strong>greater than </strong><code>1</code> and all cells must be <strong>fertile</strong>.</li>\n\t<li>The <strong>apex</strong> of an inverse pyramid is the <strong>bottommost</strong> cell of the inverse pyramid. The <strong>height</strong> of an inverse pyramid is the number of rows it covers. Let <code>(r, c)</code> be the apex of the pyramid, and its height be <code>h</code>. Then, the plot comprises of cells <code>(i, j)</code> where <code>r - h + 1 <= i <= r</code> <strong>and</strong> <code>c - (r - i) <= j <= c + (r - i)</code>.</li>\n</ol>\n\n<p>Some examples of valid and invalid pyramidal (and inverse pyramidal) plots are shown below. Black cells indicate fertile cells.</p>\n<img src=\"https://assets.leetcode.com/uploads/2021/11/08/image.png\" style=\"width: 700px; height: 156px;\" />\n<p>Given a <strong>0-indexed</strong> <code>m x n</code> binary matrix <code>grid</code> representing the farmland, return <em>the <strong>total number</strong> of pyramidal and inverse pyramidal plots that can be found in</em> <code>grid</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/22/1.JPG\" style=\"width: 575px; height: 109px;\" />\n<pre>\n<strong>Input:</strong> grid = [[0,1,1,0],[1,1,1,1]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The 2 possible pyramidal plots are shown in blue and red respectively.\nThere are no inverse pyramidal plots in this grid. \nHence total number of pyramidal and inverse pyramidal plots is 2 + 0 = 2.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/22/2.JPG\" style=\"width: 502px; height: 120px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,1,1],[1,1,1]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The pyramidal plot is shown in blue, and the inverse pyramidal plot is shown in red. \nHence the total number of plots is 1 + 1 = 2.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/22/3.JPG\" style=\"width: 676px; height: 148px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,1,1,1,0],[1,1,1,1,1],[1,1,1,1,1],[0,1,0,0,1]]\n<strong>Output:</strong> 13\n<strong>Explanation:</strong> There are 7 pyramidal plots, 3 of which are shown in the 2nd and 3rd figures.\nThere are 6 inverse pyramidal plots, 2 of which are shown in the last figure.\nThe total number of plots is 7 + 6 = 13.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>1 <= m, n <= 1000</code></li>\n\t<li><code>1 <= m * n <= 10<sup>5</sup></code></li>\n\t<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>\n</ul>\n",
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"translatedTitle": "统计农场中肥沃金字塔的数目",
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"translatedContent": "<p>有一个 <strong>矩形网格</strong> 状的农场，划分为 <code>m</code> 行 <code>n</code> 列的单元格。每个格子要么是 <strong>肥沃的</strong> （用 <code>1</code> 表示），要么是 <strong>贫瘠</strong> 的（用 <code>0</code> 表示）。网格图以外的所有与格子都视为贫瘠的。</p>\n\n<p>农场中的 <strong>金字塔</strong> 区域定义如下：</p>\n\n<ol>\n\t<li>区域内格子数目 <strong>大于 </strong><code>1</code> 且所有格子都是 <strong>肥沃的</strong> 。</li>\n\t<li>金字塔 <strong>顶端</strong> 是这个金字塔 <strong>最上方</strong> 的格子。金字塔的高度是它所覆盖的行数。令 <code>(r, c)</code> 为金字塔的顶端且高度为 <code>h</code> ，那么金字塔区域内包含的任一格子 <code>(i, j)</code> 需满足 <code>r <= i <= r + h - 1</code> <strong>且</strong> <code>c - (i - r) <= j <= c + (i - r)</code> 。</li>\n</ol>\n\n<p>一个 <strong>倒金字塔</strong> 类似定义如下：</p>\n\n<ol>\n\t<li>区域内格子数目 <strong>大于</strong> <code>1</code> 且所有格子都是 <b>肥沃的</b> 。</li>\n\t<li>倒金字塔的 <strong>顶端</strong> 是这个倒金字塔 <strong>最下方</strong> 的格子。倒金字塔的高度是它所覆盖的行数。令 <code>(r, c)</code> 为金字塔的顶端且高度为 <code>h</code> ，那么金字塔区域内包含的任一格子 <code>(i, j)</code> 需满足 <code>r - h + 1 <= i <= r</code> <strong>且</strong> <code>c - (r - i) <= j <= c + (r - i)</code> 。</li>\n</ol>\n\n<p>下图展示了部分符合定义和不符合定义的金字塔区域。黑色区域表示肥沃的格子。</p>\n\n<p><img src=\"https://assets.leetcode.com/uploads/2021/11/08/image.png\" style=\"width: 700px; height: 156px;\"></p>\n\n<p>给你一个下标从 <strong>0</strong> 开始且大小为 <code>m x n</code> 的二进制矩阵 <code>grid</code> ，它表示农场，请你返回 <code>grid</code> 中金字塔和倒金字塔的 <strong>总数目</strong> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/eg11.png\" style=\"width: 200px; height: 102px;\"> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/exa12.png\" style=\"width: 200px; height: 102px;\"> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/exa13.png\" style=\"width: 200px; height: 102px;\"></p>\n\n<pre><b>输入：</b>grid = [[0,1,1,0],[1,1,1,1]]\n<b>输出：</b>2\n<strong>解释：</strong>\n2 个可能的金字塔区域分别如上图蓝色和红色区域所示。\n这个网格图中没有倒金字塔区域。\n所以金字塔区域总数为 2 + 0 = 2 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/eg21.png\" style=\"width: 180px; height: 122px;\"> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/exa22.png\" style=\"width: 180px; height: 122px;\"> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/exa23.png\" style=\"width: 180px; height: 122px;\"></p>\n\n<pre><b>输入：</b>grid = [[1,1,1],[1,1,1]]\n<b>输出：</b>2\n<strong>解释：</strong>\n金字塔区域如上图蓝色区域所示，倒金字塔如上图红色区域所示。\n所以金字塔区域总数目为 1 + 1 = 2 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/eg3.png\" style=\"width: 149px; height: 150px;\"></p>\n\n<pre><b>输入：</b>grid = [[1,0,1],[0,0,0],[1,0,1]]\n<b>输出：</b>0\n<strong>解释：</strong>\n网格图中没有任何金字塔或倒金字塔区域。\n</pre>\n\n<p><strong>示例 4：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/eg41.png\" style=\"width: 180px; height: 144px;\"> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/eg42.png\" style=\"width: 180px; height: 144px;\"> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/eg43.png\" style=\"width: 180px; height: 144px;\"> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/23/eg44.png\" style=\"width: 180px; height: 144px;\"></p>\n\n<pre><strong>输入：</strong>grid = [[1,1,1,1,0],[1,1,1,1,1],[1,1,1,1,1],[0,1,0,0,1]]\n<b>输出：</b>13\n<strong>解释：</strong>\n有 7 个金字塔区域。上图第二和第三张图中展示了它们中的 3 个。\n有 6 个倒金字塔区域。上图中最后一张图展示了它们中的 2 个。\n所以金字塔区域总数目为 7 + 6 = 13.\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>1 <= m, n <= 1000</code></li>\n\t<li><code>1 <= m * n <= 10<sup>5</sup></code></li>\n\t<li><code>grid[i][j]</code> 要么是 <code>0</code> ，要么是 <code>1</code> 。</li>\n</ul>\n",
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